An improved method for super-helical sliding mode observer

Abstract

The present invention discloses a method for improving a superhelical sliding mode observer, comprising the following steps: Step S1, constructing a mathematical model of a permanent magnet synchronous motor; Step S2, constructing a superhelical sliding mode observer based on the mathematical model of the permanent magnet synchronous motor; Step S3, improving the operating logic conditions of the superhelical sliding mode observer, wherein the operating logic conditions include a switching function and a sliding mode gain parameter; and Step S4, performing a simulation test to obtain an output result of the superhelical sliding mode observer and determine the improvement effect of the superhelical sliding mode observer. The present invention constructs a piecewise square root hyperbolic tangent function as a switching function, which has a smooth function curve and fast response speed. When applied to the superhelical sliding mode observer, it ensures that the observed value of the back electromotive force has high sinusoidality and low jitter. An adaptive sliding mode gain that changes with the observed speed is designed to enhance the robustness of the system and further reduce system chattering. The use of a low-pass filter is eliminated, simplifying the system complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor control, and in particular relates to an improved method for a super-helical sliding mode observer. Background Art

[0002] Permanent magnet synchronous motors (PMSMs), with their small size, fast response, simple structure, reliable operation, and high power density, are widely used in applications requiring high-precision speed regulation, such as industrial drives and electric vehicles. Most control strategies for precise PMSM control require accurate rotor position information. Currently, obtaining this rotor information relies primarily on mechanical sensors. However, these position sensors are susceptible to environmental influences, increasing system complexity and degrading motor control performance. Therefore, sensorless control technology offers significant advantages.

[0003] Key approaches to sensorless control include the Luenberger observer, sliding mode observer, model reference adaptation, and Kalman filtering. The sliding mode observer, or SMO, is widely used in high-speed, sensorless PMSM control systems due to its simple structure and robustness. However, due to the inherent characteristics of sliding mode variable structure control, the SMO can produce high-frequency chattering and low sinusoidality in the observed back-electromotive force.

[0004] The most pressing issue with SMO is system chattering. Furthermore, SMO's sliding mode gain is difficult to debug and determine. A large sliding mode coefficient can cause severe chattering in sensorless control systems when the motor is running at low speeds, even leading to system instability. However, the system exhibits strong anti-interference capabilities. Conversely, a smaller sliding mode coefficient can effectively suppress system chattering, but this can reduce the system's rapid response performance. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides an improved method for a super-helical sliding mode observer.

[0006] The present invention is achieved through the following technical solutions.

[0007] The present invention provides a method for improving a super-helical sliding mode observer, comprising the following steps:

[0008] Step S1, constructing a mathematical model of a permanent magnet synchronous motor;

[0009] Step S2: constructing a super-helical sliding mode observer according to the mathematical model of the permanent magnet synchronous motor;

[0010] Step S3, improving the operating logic conditions of the super-helical sliding mode observer, wherein the operating logic conditions include a switching function and a sliding mode gain parameter;

[0011] Step S4: simulation test to obtain the output result of the super-helical sliding mode observer and determine the improvement effect of the super-helical sliding mode observer.

[0012] Preferably, the construction of the permanent magnet synchronous motor mathematical model comprises the following steps:

[0013] Set up the permanent magnet synchronous motor analysis environment;

[0014] A mathematical model of permanent magnet synchronous motor is constructed based on the permanent magnet synchronous motor analysis environment.

[0015] Preferably, the setting of the permanent magnet synchronous motor analysis environment includes: setting the induced electromotive force generated by the armature winding to have a sinusoidal change; setting the stator core magnetic circuit to not be saturated; setting the stator winding inductance and resistance to remain basically unchanged during the operation of the motor; and setting the core eddy current and hysteresis loss to be ignored.

[0016] Preferably, the model of the permanent magnet synchronous motor supports a surface-mounted three-phase permanent magnet synchronous motor;

[0017] The mathematical model of the permanent magnet synchronous motor is expressed as follows in a two-phase stationary coordinate system:

[0018] ,

[0019] Where u α and u β is the voltage in the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, R and L are the stator resistance and inductance, Ψ i is the permanent magnet flux, e and θ e are the electrical angular velocity and electrical angle.

[0020] Preferably, constructing a super-helical sliding mode observer according to a mathematical model of a permanent magnet synchronous motor comprises the following steps:

[0021] Obtain the current state equation through the permanent magnet synchronous motor mathematical model;

[0022] The current state equation is combined with the super helical algorithm and the traditional sliding mode observer to construct a super helical sliding mode observer.

[0023] Preferably, the current state equation is expressed as follows:

[0024] ,

[0025] Where u α and u β is the voltage in the two-phase stationary coordinate system, i α and i βis the current in the two-phase stationary coordinate system, R and L are the stator resistance and inductance, e α and e β is the back electromotive force in the two-phase stationary coordinate system, L d is the stator inductance of the motor;

[0026] The expression of the super-helical sliding mode observer is as follows:

[0027] ,

[0028] Where, and is the estimated value of the current, and is the current error value, sign() is the switching function, K1 and K2 are the sliding mode gains.

[0029] Preferably, the operating logic conditions of the improved super-helical sliding mode observer include: setting a piecewise square root hyperbolic tangent function as a switching function, and setting adaptive sliding mode gains K1 and K2.

[0030] Preferably, the expression of the piecewise square root hyperbolic tangent function is as follows:

[0031] ,

[0032] Where, e is the back electromotive force, s is the sliding surface;

[0033] The adaptive sliding mode gain expression is as follows:

[0034] ,

[0035] Where, is the adaptive coefficient, The reference speed is set. is the observed value of the rotational speed.

[0036] Preferably, the simulation test to obtain the output result of the super-helical sliding mode observer and determine the improvement effect of the super-helical sliding mode observer includes the following steps:

[0037] Set the inverter switching frequency, load torque and adaptive coefficient;

[0038] Set the permanent magnet synchronous motor parameters;

[0039] Perform simulations to obtain the output of the super-helical sliding mode observer based on the inverter switching frequency, load torque, adaptive coefficient, and permanent magnet synchronous motor parameters.

[0040] The improvement effect of the super spiral sliding mode observer is determined by comparing the parameters of the super spiral sliding mode observer before and after improvement.

[0041] The simulation experiment supports Matlab.

[0042] Preferably, the permanent magnet synchronous motor parameters include stator resistance, stator inductance, rated speed, rated current, moment of inertia, flux linkage, number of pole pairs and rated voltage;

[0043] The parameters of the super-helical sliding mode observer include back electromotive force and rotation speed.

[0044] The beneficial effects of the present invention are:

[0045] 1. The present invention constructs a piecewise square root hyperbolic tangent function as a switching function. The function curve is smooth and the response speed is fast. When used in a super-helical sliding mode observer, the observed value of the back electromotive force has a high sinusoidal degree and low jitter.

[0046] 2. An adaptive sliding mode gain that changes with the observed speed is designed to enhance the robustness of the system and further reduce the system chattering;

[0047] 3. The use of low-pass filter is eliminated, simplifying the system complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flow chart of a method provided by an embodiment of the present invention;

[0049] Figure 2 is a function comparison diagram provided by an embodiment of the present invention;

[0050] Figure 3 This is a system control block diagram provided by an embodiment of the present invention;

[0051] Figure 4 is a comparison diagram of back electromotive force observation values ​​provided by an embodiment of the present invention;

[0052] Figure 5 4 is a rotation speed comparison diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The technical solution of the present invention is further described below, but the scope of protection claimed is not limited to the description.

[0054] like Figure 1 As shown, a super-spiral sliding mode observer improvement method includes the following steps:

[0055] Step S1, constructing a mathematical model of a permanent magnet synchronous motor;

[0056] Constructing a mathematical model of a permanent magnet synchronous motor includes the following steps:

[0057] Set up the permanent magnet synchronous motor analysis environment;

[0058] Setting up the permanent magnet synchronous motor analysis environment includes: setting the induced electromotive force generated by the armature winding to have a sinusoidal variation; setting the stator core magnetic circuit to not be saturated; setting the stator winding inductance and resistance to remain basically unchanged during motor operation; and setting the core eddy current and hysteresis losses to be ignored.

[0059] A mathematical model of permanent magnet synchronous motor is constructed based on the permanent magnet synchronous motor analysis environment.

[0060] The model of permanent magnet synchronous motor supports surface-mount three-phase permanent magnet synchronous motor;

[0061] The mathematical model of the permanent magnet synchronous motor is expressed in a two-phase stationary coordinate system as follows:

[0062] ,

[0063] Where u α and u β is the voltage in the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, R and L are the stator resistance and inductance, Ψ i is the permanent magnet flux, e and θ e are the electrical angular velocity and electrical angle.

[0064] The back electromotive force expression is:

[0065] ,

[0066] Where, e α and e β is the back electromotive force in the two-phase stationary coordinate system, m is the permanent magnet flux, e and θ e are the electrical angular velocity and electrical angle.

[0067] From the back electromotive force expression, we can see that the back electromotive force of PMSM contains the motor speed and rotor position information.

[0068] Step S2: constructing a super-helical sliding mode observer according to the mathematical model of the permanent magnet synchronous motor;

[0069] The construction of super-helical sliding mode observer based on the mathematical model of permanent magnet synchronous motor includes the following steps:

[0070] Obtain the current state equation through the permanent magnet synchronous motor mathematical model;

[0071] The current state equation is expressed as follows:

[0072] ,

[0073] Where u α and u β is the voltage in the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, R and L are the stator resistance and inductance, e α and e β is the back electromotive force in the two-phase stationary coordinate system, L d is the stator inductance of the motor;

[0074] The current state equation is combined with the super helical algorithm and the traditional sliding mode observer to construct a super helical sliding mode observer.

[0075] The expression of the super-helical sliding mode observer is as follows:

[0076] ,

[0077] Where, and is the estimated value of the current, and is the current error value, sign() is the switching function, K1 and K2 are the sliding mode gains.

[0078] When the system is on the sliding surface and in a convergent state, , , at this time, the estimated formula of back electromotive force is:

[0079] ,

[0080] Where, and is the current error value, sign() is the switching function, K1 and K2 are the sliding mode gains.

[0081] It can be seen that the observed value of the back EMF consists of two parts. The first half is similar to the traditional sliding mode observer. The sliding mode gain K1 affects the response speed and convergence of the system. The second half is an integral term. The sliding mode gain K2 affects the jitter of the system by reducing the jitter caused by the sign function sign through integration.

[0082] After observing the back electromotive force, the high-frequency signal is filtered through a low-pass filter, the angle position information is extracted through the inverse tangent function, and then differentiated to obtain the speed information.

[0083] Step S3, improving the operating logic conditions of the super-helical sliding mode observer, wherein the operating logic conditions include a switching function and a sliding mode gain parameter;

[0084] The operation logic conditions of the improved super-helical sliding mode observer include: setting a piecewise square root hyperbolic tangent function as a switching function, and setting adaptive sliding mode gains K1 and K2.

[0085] The control principle of the sliding mode observer shows that the discontinuity of the sign function near zero and the large switching values ​​cause significant system chattering. Designing a piecewise square root hyperbolic tangent function to replace the sign function offers advantages over other solutions, including a smooth and integrable curve, fast response near zero, effective reduction of system chattering, and increased sinusoidality of the back EMF.

[0086] The expression of the piecewise square root hyperbolic tangent function is as follows:

[0087] ,

[0088] Where, e is the back electromotive force, s is the sliding surface;

[0089] The comparison image of the piecewise square root hyperbolic tangent function and the sign function is as follows Figure 2 shown.

[0090] At the same time, the sliding mode gains K1 and K2 are difficult to establish due to their numerous limitations and influences. Their magnitude determines system convergence and also affects system response speed and chattering. Therefore, it is crucial to set a sliding mode gain that varies with the control situation.

[0091] The adaptive sliding mode gain expression is as follows:

[0092] ,

[0093] Where, is the adaptive coefficient, The reference speed is set. is the observed value of the rotational speed.

[0094] The adaptive sliding mode gain K1 is larger when the motor speed differs significantly from the expected speed, which can accelerate the system's convergence and quickly bring the motor speed closer to the expected speed, enhancing the system's robustness at low speeds. K2 increases with the observed speed, increasing the system's stability.

[0095] After the super-helical sliding mode observer is improved, the observed back electromotive force has a higher sinusoidal degree, and the low-pass filter can be omitted. Without the phase delay of the low-pass filter, compensation is not required in the calculation of the estimated value of the stator position, which simplifies the system.

[0096] The control block diagram of the improved super spiral sliding mode observer system is as follows: Figure 3 shown.

[0097] Step S4: simulation test to obtain the output result of the super-helical sliding mode observer and determine the improvement effect of the super-helical sliding mode observer.

[0098] The simulation experiment supports MATLAB.

[0099] In this embodiment, a simulation experiment is performed using the Simulink module in Matlab.

[0100] The simulation test, obtaining the output result of the super-helical sliding mode observer, and determining the improvement effect of the super-helical sliding mode observer includes the following steps:

[0101] Set the inverter switching frequency, load torque and adaptive coefficient;

[0102] In this embodiment, the inverter switching frequency is set to 10kHz, a load torque of 5N∙m is added at 0.1s, and the adaptive coefficients z1=2 and z2=0.0097;

[0103] Set the permanent magnet synchronous motor parameters;

[0104] Permanent magnet synchronous motor parameters include stator resistance, stator inductance, rated speed, rated current, moment of inertia, flux linkage, number of pole pairs and rated voltage;

[0105] In this embodiment, the permanent magnet synchronous motor parameter settings are shown in the following table:

[0106]

[0107] Perform simulations to obtain the output of the super-helical sliding mode observer based on the inverter switching frequency, load torque, adaptive coefficient, and permanent magnet synchronous motor parameters.

[0108] The parameters of the super-helical sliding mode observer include back electromotive force and rotational speed.

[0109] The improvement effect of the super spiral sliding mode observer is determined by comparing the parameters of the super spiral sliding mode observer before and after improvement.

[0110] like Figure 4 As shown, comparing the super-helical sliding mode observer with a super-helical sliding mode observer using a sign function can compare the sinusoidality and smoothness of the back EMF. The back EMF using the sign function contains high-frequency jitter interference, which affects the smoothness of the motor's speed and torque. Furthermore, a low-pass filter is required to filter the high-frequency signal to effectively extract the rotor position information.

[0111] like Figure 5As shown, the super-helical sliding mode observer responds faster during low-speed motor startup, converges to the target speed more quickly, and has minimal overshoot. It also returns to the original speed more quickly and stabilizes at the target speed within 0.1 seconds after the load is connected. Compared to other control methods, it exhibits less fluctuation.

[0112] The improved super-helical sliding mode observer of the present invention has excellent speed control, fast system response, good chatter suppression, and can quickly react to external interference and approach stability. Compared with other control methods, it has faster convergence and better control effect.

Claims

1. A super-helical sliding mode observer improvement method, characterized in that: The steps include: Step S1, constructing a mathematical model of a permanent magnet synchronous motor; Step S2: constructing a super-helical sliding mode observer based on the mathematical model of the permanent magnet synchronous motor, including: obtaining a current state equation through the mathematical model of the permanent magnet synchronous motor; combining the current state equation with the super-helical algorithm and the traditional sliding mode observer to construct a super-helical sliding mode observer; Wherein, the current state equation is expressed as follows: , Where u α and u β is the voltage in the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, R and L are the stator resistance and inductance, e α and e β is the back electromotive force in the two-phase stationary coordinate system, L d is the stator inductance of the motor; the expression of the super-helical sliding mode observer is as follows: , Where, and is the estimated value of the current, and is the error value of the current, sign() is the switching function, K1 and K2 are the sliding mode gains; Step S3, improving the operating logic conditions of the super-helical sliding mode observer, wherein the operating logic conditions include a switching function and a sliding mode gain parameter; the operating logic conditions of the improved super-helical sliding mode observer include: setting a piecewise square root hyperbolic tangent function as the switching function, and setting adaptive sliding mode gains K1 and K2; The expression of the piecewise square root hyperbolic tangent function is as follows: ， Where, e is the back electromotive force, s is the sliding surface; The adaptive sliding mode gain expression is as follows: ， Where, is the adaptive coefficient, The reference speed is set. is the observed value of the rotational speed; Step S4: simulation test to obtain the output result of the super-helical sliding mode observer and determine the improvement effect of the super-helical sliding mode observer.

2. The method for improving a super spiral sliding mode observer according to claim 1, wherein: The construction of the permanent magnet synchronous motor mathematical model comprises the following steps: Set up the permanent magnet synchronous motor analysis environment; A mathematical model of permanent magnet synchronous motor is constructed based on the permanent magnet synchronous motor analysis environment.

3. The improved method for super spiral sliding mode observer according to claim 2, characterized in that: The setting of the permanent magnet synchronous motor analysis environment includes: setting the induced electromotive force generated by the armature winding to have a sinusoidal variation; setting the stator core magnetic circuit to not be saturated; setting the stator winding inductance and resistance to remain basically unchanged during the operation of the motor; and setting the core eddy current and hysteresis loss to be ignored.

4. The improved method for super spiral sliding mode observer according to claim 2, characterized in that: The model of the permanent magnet synchronous motor supports surface-mount three-phase permanent magnet synchronous motor; The mathematical model of the permanent magnet synchronous motor is expressed as follows in a two-phase stationary coordinate system: ， Where u α and u β is the voltage in the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, R and L are the stator resistance and inductance, Ψ i is the permanent magnet flux, e and θ e are the electrical angular velocity and electrical angle.

5. The improved method for super spiral sliding mode observer according to claim 1, characterized in that: The simulation test, obtaining the output result of the super-helical sliding mode observer and determining the improvement effect of the super-helical sliding mode observer, includes the following steps: Set the inverter switching frequency, load torque and adaptive coefficient; Set the permanent magnet synchronous motor parameters; Perform simulations to obtain the output of the super-helical sliding mode observer based on the inverter switching frequency, load torque, adaptive coefficient, and permanent magnet synchronous motor parameters. The improvement effect of the super spiral sliding mode observer is determined by comparing the parameters of the super spiral sliding mode observer before and after improvement. The simulation experiment supports Matlab.

6. The improved method for super spiral sliding mode observer according to claim 5, characterized in that: The permanent magnet synchronous motor parameters include stator resistance, stator inductance, rated speed, rated current, moment of inertia, flux linkage, number of pole pairs and rated voltage; The parameters of the super-helical sliding mode observer include back electromotive force and rotation speed.

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